Complex Numbers (Book)

Blog Calendar

◄ June ► 2023
S	M	T	W	T	F	S
				1	2	3
4	5	6	7	8	9	10
11	12	13	14	15	16	17
18	19	20	21	22	23	24
25	26	27	28	29	30
Archive				RSS

About This Author

Contact Me

Come closer.

Complex Numbers

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

June 26, 2023 at 8:54am

#1051607

In the Game

Everyone has an opinion on video games. Most of them are wrong.

gaming, in kids' own words

I'm going to go ahead and note the precious no-caps headline, and then forget about it.

A few weeks ago, I interviewed Dr. Rachel Kowert about the new genre of alarmist rhetoric around kids’ pandemic gaming and screen time.

As is often the case, I'm behind the curve, here; this article is from early 2021. But the "alarmist rhetoric" has been going on since long before the pandemic; enforced social isolation only changed the narrative a bit.

You might not have kids, and you might not spend much time worrying about gaming.

I don't, and I'm too busy playing games to worry about them.

But you can still recognize that as a society, we often spend a lot of time worrying about how a cultural product is affecting a group of people — kids, teen girls, grown-ass women — and very little time actually talking to the people actually consuming it.

Right, because teen boys and men can be safely ignored.

The problem, then, is that some people don’t want things to be complicated. They don’t want to hear people talk about why they like things, because if they listen long enough, it will challenge neat understanding of things that are “good” and “bad” — especially when it comes to children, or teens, or women.

I'm going to spend the rest of this entry not being salty about the demographics there.

I'll just note that this bit is otherwise pretty insightful, and argues against the pervasive good/bad binary. It's as if the great philosophers Beavis and Butt-Head live in people's minds, where everything is either cool, or sucks, and there's no nuance. One star or five stars, never anything in between.

Kids don’t know everything. But they often do know themselves. So I wanted to hear them talk about their own relationship to the games they play: what they like about it, when they like to play, how games make them feel, who they like to play with, and how they respond to anxiety about their gaming/screen time.

So, most of the article does just that. I won't highlight much from the interviews, but I found them interesting.

There's just one caveat:

I gave adults a list of potential questions, and then asked them to transcribe answers in as close to their kids’ voice as possible. Some of the answers have been shortened, but none of the wording has.

I'd like to believe that, but this is, like, hearsay of hearsay. Some of the "voices" are questionable to me. So I wouldn't take any of them as accurate; some might be flat-out lying.

I won't exacerbate that situation by quoting a lot from the actual interviews; just highlight a couple that I found to be interesting, whether it's actually a kid's "voice" or not.

(5 year old kid) I hope you really enjoy video games too. They're invented to be really cool.

They're invented to be engaging, rewarding, and at least borderline addictive. I say this as a gamer, but I'm also an adult (at least by chronology).

(15 year old kid) Gaming is so new that there's no conclusive evidence yet to prove if it's actually harmful. It feels like they’re just trying to control us and tell us what to do.

Now this, I can believe coming from a 15 year old.

(13 year old kid) People need to make sure they don’t get correlation and causation mixed together.

Which is what I've been saying. I'm tempted to not believe he actually said that, but other things in that kid's interview make me think he's rather advanced for a 13 year old.

There's a lot more at the link. One final point, though: a lot of these kids focus on the social aspects of gameplay. I prefer playing solo games, myself. Unlike these kids, I followed the evolution of computer games from text-based adventures all the way to near-VR experiences. I've had a lot of good experiences playing multiplayer games, but I also think there's a toxic culture there. Not just online trolls, but the whole conversion of a leisure activity to cutthroat competition.

I don't know. Maybe you think I don't get to have an opinion on the subject, because I don't have kids. That's your prerogative, of course, but these kids are part of the society I live in, so I do have an opinion.

So do they.

4 Like • Comment • View 2 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.